Educational technique needs a philosophy, which is a matter of faith rather than of science. - Hans Freudenthal

[The goal of developmental research is to] consciously experience, describe and justify the cyclic process of development and research so that it can be passed on to others in such a way that they can witness and relive the experience.

Science should be distinguished from technique and its scientific instrumentation, technology. Science is practised by scientists, and techniques by ‘engineers’ — a term that in our terminology includes physicians, lawyers, and teachers. If for the scientist knowledge and cognition are primary, it is action and construction that characterises the work of the engineer, though in fact his activity may be based on science. In history, technique often preceded science.

Vertical mathematising is the most likely part of the learning process for the bonds with reality to be loosened and eventually cut.